From loom spaces to veering triangulations

Abstract

We introduce loom spaces, a generalisation of both the leaf spaces associated to pseudo-Anosov flows and the link spaces associated to veering triangulations. Following work of Guéritaud, we prove that there is a locally veering triangulation canonically associated to every loom space, and that the realisation of this triangulation is homeomorphic to ${\mathbb{R}}^3$.

46 pages, 38 figures and subfigures. v4 - corrects a mistake in the definition of between (Definition 6.16)